Iran has freed a University of Melbourne academic who had been detained for more than two years.

Iran state TV reported that Kylie Moore-Gilbert, an Islamic studies lecturer who was sentenced to 10 years in prison despite no evidence of her alleged crimes, had been released after 804 days.

The 33-year-old was “swapped” for three Iranian prisoners who were in custody abroad.

It came almost a month after Dr Moore-Gilbert was feared missing after being moved from Iran’s notorious Qarchak prison to an unknown location. It was later identified as Evin Prison, where she had spent most of her time since her 2018 arrest.

Australian Foreign Minister Marise Payne confirmed Dr Moore-Gilbert was on her way back to Australia.

Tweet from @MarisePayne

“I wish Dr Moore-Gilbert well in her recovery and her return to life in Australia,” Senator Payne said.

“No doubt, as she recovers, she will draw on the same strength and determination that helped her get through her period of detention.”

In a statement released on social media, Prime Minister Scott Morrison also welcomed Dr Moore-Gilbert’s release.

“I spoke to Kylie this morning. It was wonderful to hear her voice and I look forward to seeing her after her return,” he said.

“We have always rejected her conviction and detention and I join with all Australians in praising Dr Moore-Gilbert and her family for their courage, strength and patience as we have all worked tirelessly together to secure her release.”

Dr Moore Gilbert also released a statement, thanking the Australian government and diplomats for securing her release.

“Thank you also to all of you who have supported me and campaigned for my freedom, it has meant the world to me to have you behind me throughout what has been a long and traumatic ordeal,” she said.

“I have nothing but respect, love and admiration for the great nation of Iran and its warm-hearted, generous and brave people.”

Tweet from @madd_sarah

Dr Moore-Gilbert said it was bittersweet to depart Iran, despite the injustices she was subjected to.

“I came to Iran as a friend and with friendly intentions, and depart Iran with those sentiments not only still intact, but strengthened,” she said.

Iranian state TV released footage early Thursday morning (Australian time) showing the Australian-British academic in a grey hijab in what appeared to be a greeting room at Tehran airport.

Tweet from @yjc___agency

She wore a blue face mask under her chin.

The three men released in exchange for her freedom were described by state TV as “economic activists”.

Footage showed them with Iranian flags over their shoulders.

A website affiliated to state TV said earlier the three Iranians who had been held abroad “on baseless charges” – reportedly for trying to flout US sanctions imposed on the country – had been exchanged for Dr Moore-Gilbert.

Kylie Moore-Gilbert, centre inside van, has been held in Iran since September 2018. Photo: AAP

Dr Moore-Gilbert was arrested at Tehran airport by Iran’s Revolutionary Guards In September 2018, and accused of espionage.

Since then, she has spent most of her days in solitary confinement in Evin Prison and was transferred to Qarchak Women’s Prison a few months ago.

The prison has been described by some as one of the most dangerous in Iran due to its inhumane medical and psychological conditions.

Iran’s elite Revolutionary Guards have arrested dozens of dual citizens in recent years, mostly on espionage charges.

Senator Payne has previously said Australia did not accept the spying charges.

Dr Moore-Gilbert has also vehemently denied the charges and maintained her innocence.

Friends and colleagues of Dr Moore-Gilbert were over the moon at news of her freedom.

“An innocent woman is finally free. Today is a very bright day in Australia indeed,” they said said in a statement.

-with AAP